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Abstract
This paper presents an extensive parameter study of a non-intrusive and non-seeded laser diagnostic method for measuring one dimensional (1D) rotational temperature of molecular nitrogen (N2) at 165 - 450 K. Compared to previous efforts using molecular oxygen, here resonantly ionized and photoelectron induced fluorescence of molecular nitrogen for thermometry (N2 RIPT) was demonstrated. The RIPT signal is generated by directly probing various rotational levels within the rovibrational absorption band of N2, corresponding to the 3-photon transition of N2 (${X^1}\mathrm{\Sigma }_g^ + ,v = 0 \to {b^1}{\mathrm{\Pi }_u},v^{\prime} = 6$) near 285 nm, without involving collisional effects of molecular oxygen and nitrogen. The photoionized N2 produces strong first negative band of N2+ (${B^2}\mathrm{\Sigma }_u^ +{-} {X^2}\mathrm{\Sigma }_g^ + $) near 390 nm, 420 nm, and 425 nm. Boltzmann analyses of various discrete fluorescence emission lines yield rotational temperatures of molecular nitrogen. By empirically choosing multiple rotational levels within the absorption band, non-scanning thermometry can be accurately achieved for molecular nitrogen. It is demonstrated that the N2 RIPT technique can measure 1D temperature profile up to ∼5 cm in length within a pure N2 environment. Multiple wavelengths are thoroughly analyzed and listed that are accurate for RIPT for various temperature ranges.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Non-intrusive optical and laser-based thermometry methods are of great importance for measurement of thermal properties in nonreacting high-speed gaseous flows, since conventional physical probes and/or thermal couples can significantly perturb the flow-field in supersonic and hypersonic regimes [1–3]. Quantification of aerodynamic heating arising from the boundary layer at high Mach numbers is critical for thermal protection system design of test vehicles and their associated aerothermal structures [4]. Even more critically, the real gas effects and possible plasma generations in these environments are of great interest. Additionally various computational models and calibrations require experimental measurements of thermal profiles under realistic conditions. [5,6]
Current non-intrusive gas-phase thermometry techniques include, but not limited to, planar laser induced fluorescence (PLIF), tunable diode laser absorption spectroscopy (TDLAS), filtered Rayleigh scattering (FRS), and coherent anti-stokes raman spectroscopy (CARS). etc. While, they have all been successfully demonstrated to enable non-intrusive thermometry measurements in high-speed ground test facilities; they have some inherent limitations. PLIF relies upon the use of tracer molecules, which could possibly modify flow chemistry and small-scale flow features [7,8]. TDLAS is a path integration technique that make it difficult to filter unwanted noise from wall boundary layers and other fluid dynamic anomalies that lie outside the region-of-interest (ROI) [9,10]. Filtered Rayleigh scattering needs relatively high number density to have strong signal to noise ratio [11]. Though non-seeded and non path-integrated, CARS demands precise optical alignment of multiple laser beams and is sensitive to facility vibrations and noise, complicating implementation in ground test facilities. [12]
Molecular oxygen (O2) based RIPT (O2 RIPT) was previously introduced and utilized for 1D temperature measurements in plasmas and gaseous flows [2,13]. In O2 RIPT, a single laser pulse resonantly ionizes molecular oxygen by resonant enhanced multiphoton ionization (REMPI) and subsequently drives the photoelectrons to enable electron impacted excitation and subsequent ionization of local nitrogen molecules. The emitted photons from the ionized nitrogen are analyzed to deduce gas temperature from Boltzmann plots of ro-vibrational populations of molecular oxygen, by directly relating to the two-photon transitional line strengths of the corresponding O2 resonance. [14–18] Additionally, the spatially broad photoelectron distribution enables 1D thermometry both upstream and downstream of the laser focal volume. While advantageous for being seedless in nonreacting flow diagnostics, a limitation of O2 RIPT is the requirement for molecular oxygen, restricting applicability in oxygen-free environments.
Regarding ground-based test facilities, the standard threshold for hypersonic flow regime’s is above Mach 5. At Mach 5 conditions, the criterion for standard air requires heating to avoid liquification of O2 within the flow expansion process. Liquification and subsequent solidification of O2 generates small ice-like particles that can greatly disrupt the flow characteristics and potential damage the facility or test article within the test section [19]. To circumvent this, many hypersonic test facilities run pure N2 media (i.e., AEDC Tunnel 9), as the liquefaction point of N2 is below that of O2. Furthermore, heating is still required, but the heating power is much less than if a standard air gas medium was used. The reduced heating requirement of pure N2 gas mediums results in lower operational costs, and lower material costs; for more exotic materials would be needed to manage the increased thermal induced fatiguing and creep from higher heating for standard air [20–22].
This work establishes and demonstrates a non-intrusive, seedless one-dimensional (1D) N2-based resonantly ionized photoemission thermometry (N2 RIPT) technique for nonreactive flows. N2 RIPT resonantly ionizes molecular nitrogen for induced photoemissions; thus, it could be applied in either pure nitrogen or standard air. Compared to O2 RIPT, N2 RIPT fundamentally differs by directly resonantly ionizing molecular nitrogen without involvement of secondary ionizations, resulting in similar photoemissions of the first negative band in N2. Since the rotational levels of molecular nitrogen are directly probed, rotational N2 temperature measurement is achieved.
2. N2 photoemissions via REMPI
Figure 1 shows the REMPI spectra in molecular nitrogen using ultraviolet (UV) laser excitation via resonant multi-photon absorption transitions from the ground state ${N_2}({{X^1}\mathrm{\Sigma }_g^ + ,v = 0} )$ state up to various intermediate states, proceeding to a photo-ionization mechanism that normally consists of one or two ionization steps [24,25]. It can be found in literature that the range between 275 nm to 290 nm laser emissions contain the strongest of the N2 resonant absorption wavelengths [26–28]. The spectra are for the ${N_2}({{b^1}{\mathrm{\Pi }_u},\textrm{}v = 6} )$ absorption band that corresponds to the b1 band head representing the intermediate REMPI transition used in this study [29]. The two strongest resonant transitions are the 2-photon absorption to the ${N_2}({{a^1}{\mathrm{\Pi }_g}} )$ and the 3-photon absorption to the ${N_2}({{b^1}{\mathrm{\Pi }_u}} )$ intermediate states, with band heads at ${N_2}({{a^1}{\mathrm{\Pi }_g},\textrm{}v = 1} )$ (approximately 283.05 nm), and ${N_2}({{b^1}{\mathrm{\Pi }_u},\textrm{}v = 6} )$ (approximately 284.8 nm) respectively [28,30,31]. This study utilizes the ${N_2}({{b^1}{\mathrm{\Pi }_u},\textrm{}v = 6} )$ intermediate state.
Fig. 1. N2 ultraviolet laser excitation spectrum at standard temperature and pressure, with labeled b1 band head. [23]
Compared to O2 RIPT, the N2 RIPT technique uses a (3 + 1) REMPI scheme: (1) 3-photon excitation step from ground state to intermediate state, and (2) 1-photon ionization to produce free photoelectrons. Specifically, the 3-photon resonant absorption band, ${N_2}({{X^1}\mathrm{\Sigma }_g^ + ,v = 0 \to {b^1}{\mathrm{\Pi }_u},v^{\prime} = 6} )$ used in this study occurs around 285 nm [28,32]. The ${N_2}({{b^1}{\mathrm{\Pi }_u},\; v^{\prime} = 6} )$ absorption band was chosen for its temperature sensitivity and demonstrated strong photoemissions post-excitation. It should be noted that N2 REMPI, specifically the 3 + 1 scheme used here, inherently suffers from collisional influenced processes at near atmospheric pressures. The collisional processes include the deactivation of the REMPI intermediate state during the laser pulse, which may preclude the ionization step. Effectively this requires another admission of a photon to permit the N2 molecule to reach the excited state, thus resulting in the (3 + 1) becoming a (3 + 2) scheme. [33]. However, the emission intensity increases linearly with pressure, thus it is possible to correct for increased photoemission in areas of low pressure that will undergo the (3 + 1) scheme relative to the (3 + 2) scheme [33].
To achieve N2 RIPT, specifically chosen rotational peaks within the N2(${{X^1}\mathrm{\Sigma }_g^ + ,v = 0 \to {b^1}{\mathrm{\Pi }_u}}$, $v^{\prime} = 6$) absorption band are resonantly excited to ionize N2 molecules via a (3 + 1) or (3 + 2) REMPI scheme given by Eq. (1) and Eq. (2), respectively.
where, $h{\nu _{REMPI}}$ is the photon used to resonantly ionize N2 and ${e^ - }$ is the emitted photoelectron. The recombination of electrons and molecular nitrogen ions produces emissions of the first negative band of $N_2^ + ({{B^2}\Sigma _u^ +{-} {X^2}\Sigma _g^ + } )$ or further decay by first positive band.First negative band:
First positive band:
where, $h{\nu _{{1^ - }}}$ is photoemission from the first negative band of N2, and $h{\nu _{{1^ + }}}$ is photoemission from the first positive band of N2. The first negative band are at three distinct peaks (Δv0, ∼390 nm; Δv2, ∼425 nm; Δv1, ∼430 nm), resulting from the $1 \to 0$, $2 \to 1$, and $1 \to 1$ transitions, respectively. For N2 RIPT the resulting N2 photoemission strength is influenced by both pressure and number density, however this study will only investigate the capacity of using nitrogen’s first negative band emissions for thermometry applications at standard pressure (760 Torr). To perform a rotational state distribution analysis on N2 and subsequently determine the temperature from the resulting N2 first negative photoemissions, it is essential to acquire a rotationally resolved spectrum of the molecular nitrogen. Additionally, accurate three-photon transition cross-sectional data is required to effectively identify appropriate peaks for analysis.3. N2 REMPI structures
The (3 + 1) and (3 + 2) REMPI structures of N2 are described in detail in previous literature [28,34–36]. A brief summary is given here. Both the ground state, N2(X1Σ) and the excited state, N2(B2Π) can both be described by Hund’s case (a), in which hyperfine splitting is apparent in both the ground and excited states. The theoretical line strength factors, $S({J^{\prime},J^{\prime\prime}} )$ for 3-photon transitions, which are relevant to the ${N_2}({{X^1}\mathrm{\Sigma }_g^ + ,v = 0 \to {b^1}{\mathrm{\Pi }_u},v^{\prime} = 6} )$ absorption band studied here, have been previously derived [34,37]. The modified 3-photon transitional line strength factors are given by Eq. (5)-(7) for the P, Q, and R-transitions, respectively.
Assuming local thermal equilibrium (LTE) conditions, the relative amplitude/strength of the individual ro-vibronic lines for the 3-photon resonant transition can be calculated using Eq. (8).
where, F is the global factor that accounts for vibrational and electronic transition probabilities independent of the rotational transitions, $g({J^{\prime\prime}} )$ is the nuclear spin statistical weight, $S({J^{\prime},J^{\prime\prime}} )$ is the multi-photon line strength factor, and $exp({ - {E_{rot}}/kT} )$, is the Boltzmann rotational populational distribution. It should be noted, the nuclear spin statistical weight $g({J^{\prime\prime}} )$ is 2 for even $J^{\prime\prime}$ and 1 for odd $J^{\prime\prime}$. A similar model has been previously developed in literature and was used for photoemission fitting to the simulated spectrum for temperature assignment. The model from literature exhibited high accuracy from 150 K – ∼600 K [29].The N2 REMPI absorption spectrum is made up of congested contributions from the P, Q, and R-branches, peak selection is not a trivial matter, as the individual contributions may vary independently of each other. Thus, the simulated spectrums were instrumental in gaining insight on population distributions and contributions from each branch of the absorption band. This model is shown in Fig. 2 for 180, 293, and 460 K. Using this model, peaks were identified that had relevant population distributions at the various temperature test points and demonstrated temperature sensitivity. Furthermore, the model shows that as temperature increases population distributions trend towards higher rotational states, resulting in increased structure in the spectrum. Similar to O2 RIPT, suitable peaks change depending on temperature of the test medium. Furthermore, while not graphically shown, it was found the P and Q branches contribute to distinct peaks, while the R-branch has its own distinct peaks. A more in-depth look at Fig. 2 reveals that the 293 and 460 K spectrums share some peaks that do not vary as a function of temperature, but the population distributions trend so greatly towards the ground state at 150 K that all peaks are affected, furthering the importance of peak selection.
Fig. 2. Normalized theoretical N2 REMPI spectra for 150, 293, and 460 K, showing various rotational levels of molecular nitrogen.
Additionally, while RIPT is driven by N2 REMPI and recombinative N2 first negative photoemissions, the intensity of the nitrogen fluorescence $({\Delta {v_0},\Delta {v_1},\Delta {v_2}} )$ demonstrates a strong correlation with the (3 + 1) or (3 + 2) REMPI scheme [29,33]. This correlation enables the direct application of the modeled spectra, in conjunction with the prior investigation involving calculated emission intensity as described by Eq. (8). This approach facilitates the identification of several resonant wavelengths of significance for utilization in the calibration study.
4. Experimental setup
Similar to O2 RIPT calibration study, a calibration study using pure N2 and air was conducted at 165, 230, 293, 376, and 455 K in a gas cell. A depiction illustrating the general setup for the N2 RIPT calibration experiment is presented in Fig. 3. Employing the second-harmonic of an Nd:YAG laser (Continuum Surelite SL-10), characterized by an 8 ns pulse duration, a repetition rate of 10 Hz, and a lasing energy of 220 mJ/pulse, as the pumping source for a dye laser (Continuum ND6000). The dye laser employed a combination of rhodamine 590 and rhodamine 610 to generate laser light centered around 570 nm, with a linewidth of 0.02 cm-1.
Fig. 3. Schematics of N2 RIPT calibration experiment. Both liquid nitrogen chiller and conduction heating tapes were used to vary the temperature.
The dye laser underwent frequency doubling to generate an ultraviolet (UV) beam, which was facilitated by an auto-tracker (Continuum UVT-1) to ensure consistent conversion efficiency through the frequency doubling crystal. The resultant UV beam carried an energy of around 10 mJ/pulse, spanning the range from 284 to 286.5 nm. The UV beam was focused using a fused-silica spherical lens with focal length of +150 mm, which generated a RIPT fluorescence line. The line was centered in a cylindrical, fused-silica glass cell. The estimated spot size of the focused laser beam is about 100µm in diameter.
Emission spectra were gathered using a pair of +100 mm spherical fused silica lenses, which focus the light onto the slit of a spectrometer (Princeton Instruments, 600 grooves per millimeter [gr/mm], blazed at 500 nm with a 50 µm slit width. The spectral data was then captured using an intensified scientific camera (PI-MAX4 1024f), which possessed a sensor size of 1024 × 1024 pixels. To capture the short lived first negative band, the scientific camera was set to a 50 ns exposure time and captured 10 images at 10 accumulations each. Additionally, the spectrometer was centered at 405 nm to capture the three distinct first negative peaks as previously mentioned.
To ensure uniformity of species number density within the area of interest and prevent localized heating, a continuous flow of pure nitrogen gas was supplied to the cell at a rate of 0-50 liters per minute (L/min) via an electronic flow controller. Depending on the desired calibration temperature the air passed through either a flow heater or through a custom-built flow-chiller. These setups allowed for temperature adjustments spanning from 160 to 470 K. Monitoring of the cell temperature was facilitated by a K-type thermocouple, which ensured adherence to a tolerance level of ±1% in relation to the set point.
5. Results and discussions
5.1 N2+ emission spectra via N2 RIPT
Visualized in Fig. 4 and 5 are the N2+ emission spectra at 165 and 230 K. The rest of spectra at the remaining calibration temperatures of 293, 376, and 455 K are given in Supplement 1. The spectra collected at the selected wavelengths over the range of temperatures showed similar features. Changes in the bands emitted signal intensity were the only observable change. At all temperatures, there are only two distinct peaks that are shown in the spectra (Δv0, 390 nm; Δv1, 430 nm), resulting from the $1 \to 0$, and $1 \to 1$ transitions, respectively. This indicates the ionization region is cooler than the O2 RIPT ionization. This is due to the higher ionization energy requirements for N2 compared to O2 thus, more of the laser energy is used to achieve ionization than those to be used for further heating of the plasma.
Fig. 4. N2+ emission spectra at 165 K at selected excited wavelengths. The excitation wavelength is highlighted in blue on the top of each emission spectrum. The emission intensity is in arbitrary units.
Fig. 5. N2+ emission spectra at 230 K at selected excited wavelengths. The excitation wavelength is highlighted in blue on the top of each emission spectrum. The emission intensity is in arbitrary units.
Due to the congestion of the P, Q, and R-branches in the ${N_2}({{b^1}\mathrm{\Pi }} )$ resonant band, all peaks are temperature sensitive. The laser used in this study was unable to individually resolve the P and Q branches, but the R-branch was able to be resolved independently. However, the relevant population distributions in the R-branch result in very weak signal, and only become more relevant at very high temperatures outside of those tested in this study. Thus, the peaks selected for temperature determination are a result of the P and Q-branch congested transitions.
5.2 Temperature determination by individual vibrational emission bands
Similar to O2 RIPT, the aforementioned $N_2^ + ({{B^2}\Sigma _u^ +{-} {X^2}\Sigma _g^ + } )$ photoemission spectra were post-processed, including the raw images averaging, background subtraction. A study was conducted for identification of possible groups that exhibited a linear fit of high correlation and thus an accurate temperature determination, from a pure signal intensity analysis standpoint. The peak signals for 165 K are visualized in Fig. 6(a and b). It was found for N2 RIPT the raw signal intensity deviates substantially from the processed signal properties; thus, a pure visual inspection of the raw signal intensities is not possible. This is mainly attributed to the 3-photon line strength factors deviating from the predicted theoretical values, and the resulting polynomial (2nd order) law fit used to correct for them as mathematically expressed in Eq. (8)–(10). The 390 nm and 430 nm signal intensities for 273, 376, and 455 K are shown in Supplement 1.
Fig. 6. Integrated individual peak signal values for (a) Δv0, 390 nm, (b) Δv1, 430 nm, and temperature determinations at (c) Δv0, and (d) Δv1 for an environmental temperature of 165 K.
Fig. 7. Integrated individual peak signal values for (a) Δv0, 390 nm, (b) Δv1, 430 nm, and temperature determinations at (c) Δv0, and (d) Δv1 for an environmental temperature of 230 K.
Four wavelengths at each calibration temperature are applied to Eq. (8) to fit a Boltzmann distribution for rotational temperature assignment. When more and less than four wavelengths were examined for temperature fitting, it was found that fitting by four wavelengths results in the highest fitting accuracy. The resultant N2 RIPT measurements of the 390 and 430 nm peaks at 165 K are shown in Fig. 6(c) and (d). It was found that the Δv0 (390 nm) peak yielded approximate temperature fits within ±10 K, and all have a high coefficient of correlation (R2 > 97%). The Δv1 (430 nm) peak yielded approximate temperature fits within ±25 K, and still maintained a relatively high coefficient of correlation (R2 > 96%). Suggesting that there exists a very linear relationship between the Δv0 (390 nm) peak and the N2+ photoemissions and resonant excited N2. The Δv1 (430 nm) peak demonstrates a linear relationship but is not suitable for temperature determination due to relatively high error in the temperature assignments. Additionally, the Δv1 (430 nm) predicted temperature trended to overshoot the actual cell temperature, and no such relationship or trend existed with the Δv0 (390 nm) peak. It should be noted the Δv1 (430 nm) signal was typically an order of magnitude or more less than the Δv0 (390 nm) peak signal, which results in worse SNR and could have contributed to the relatively high temperature error. N2 RIPT measurements for 230 K is shown in Fig. 7. Data for 293, 376, and 455 K are in Supplement 1. The acquired N2 RIPT temperatures at each emission peak for all calibration temperatures are tabulated in Table 1 along with the error difference between experimentally determined and actual cell temperatures.
Table 1. Results for specific N2+ fluorescence bands (Δv0, and Δv1) for N2 RIPT
Through the studies of the individual emission peaks from the first negative band of N2+, it is proven that using the correct transition peak N2 RIPT is a viable, non-seeded, non-intrusive thermometry technique for resolving temperature gradients with sufficiently accuracy. Compared to O2 RIPT, a few key points of the analysis are,
- (1) the Δv1 (430 nm) peaks demonstrated low accuracy, with an average error between expected and experimentally measured temperatures of 11.22%. Additionally, it trends to over-predict low temperatures (<293 K) and under-predict high temperatures (>293 K), with the max difference in experimental and expected being (+62.69) and (-27.00) K respectively. It can be understood as that Δv1 of $1 \to 1$ transitions are of higher rotational states such that the signal would weaken at low temperatures.
- (2) The Δv0 (390 nm) peak exhibits the best capability of accurate thermal measurements, with the highest percent error difference between expected and experimental values being 3.14%, with an average error of 1.06%.
The excited rotational temperature of a molecule is typically relatively quick to respond to medium temperature changes, this inherent characteristic is due to the fundamental physics where the rotational temperature is not dependent on extrinsic events occurring outside the molecule’s immediate region, thus the direct thermal energy of the environment is typically accounted for almost instantaneously by rotational states. [38] Furthermore, it is shown that for the Δv0 (390 nm) peak the rotational state is representative of near true medium temperatures.
5.3 Temperature determination by integrated first negative emission band
To expand N2 RIPT’s applicability, useability, and enable measurements across a 1D line as in O2 RIPT, the signal used fitting to a Boltzmann distribution is found via integrating along the first negative band $N_2^ + ({{B^2}\Sigma _u^ +{-} {X^2}\Sigma _g^ + } )$, (370 to 435 nm). It means the elimination of the spectrometer from the setup and instead utilizing an optical bandpass filter for direct imaging. Figure 8 visualizes the peak intensity values found from the aforementioned integration scheme for calibration wavelengths at 165 and 230 K. Data for 293, 376, and 455 K are in Supplement 1. An inspection of Fig. 8(a) and (b) suggests that the integrated peak intensity values trend towards the Δv0 emission. This is expected as its emission intensity strength dominates the Δv1 band, typically by an order of magnitude or greater. Using an iterative approach to find peaks that could relate temperature, the best fit was found from a selected group of the integrated signal intensities, and fitted to a Boltzmann plot to assign a vibrational temperature measurement. The iterative approach used sometimes resulted in hundreds of peak group combinations until an ideal set was found.
Fig. 8. Integrated N2+ Boltzmann temperature assignments for (a) 165 K, (b) 230 K and corresponding Boltzmann plots (c) 165 K and (d) 230 K.
The Boltzmann plots in Fig. 8(c) and (d) show the temperature determination for the integrated signals at all calibration temperatures. The plots show high linearity among the four selected rotational lines for temperatures of 165, 230, 293, 376, and 455 K, thus enabling accurate thermal measurements to be achieved. Furthermore, this suggests that direct imaging of the N2+ emission is not only viable, but the preferred method for N2 RIPT measurements.
Compared to O2 RIPT, Table 2 shows the suggested wavelengths for the temperature measurements using N2 RIPT, with comparison between N2 RIPT measurement and thermocouples. A four-wavelength excitation scheme is suggested to achieve good linearity and limited experimental complexity. The capability to direct image the photoemissions is important as it enables realizes the 1D line potential in RIPT based measurements, and requires only an intensified gated camera, thus reducing experiment setup time, complexity, space, and expense. A similar measurement accuracy was achieved for slightly different temperature range. A slightly worse accuracy for lower temperature (< 250 K) was obtained than O2 RIPT, which is mainly due to the more complex nature to calculate 3-photon transitions of N2.
Table 2. Expected and experimental temperatures from N2 RIPT integrated emission study
6. Conclusions
In this work, nitrogen based and REMPI induced resonantly ionized photoemission thermometry (N2 RIPT), a non-intrusive, non-seeded technique is established and verified through a detailed calibration analysis. The dominant mechanism of plasma generation is REMPI, which is a highly nonlinear process that results in minimal deposited energy and disturbances to the surrounding environment, allowing for applications in highly sensitive areas. Furthermore, N2 RIPT utilizes resonant wavelengths to selectively excite various rotational bands of nitrogen to weakly ionize a medium gas that contains some mass fraction of nitrogen molecules. Through multiphoton ionization process, the first negative band of N2+ is created; subsequent deexcitation yields photoemissions in the visible region from 390 to 430 nm. The resulting emissions are processed and fitted to a Boltzmann distribution that yields a temperature measurement.
A discrete analysis of the emissions of the individual transitions band was conducted for the $N_2^ + ({{B^2}\Sigma _u^ +{-} {X^2}\Sigma _g^ + } )$ transition. Additionality, the N2 RIPT generated ionization is a relatively cold plasma only displaying emissions (Δv0, ∼390 nm; Δv1, ∼430 nm) that result from the $0 \to 1$ and $1 \to 1$ transitions respectively. Sets of resonant wavelengths that correspond to specific rotational peaks within the 3-photon ${N_2}({{X^1}\mathrm{\Sigma }_g^ + ,v = 0 \to {b^1}{\mathrm{\Pi }_u},v = 6} )$ absorption transition and demonstrated high-temperature sensitivity and strong photoemission signal at various temperature setpoint were found through an iterative process and the results tabulated in Table 3. It has been shown through the discrete analysis, the Δv0 dominates emissions and produces accurate experimental gas temperature measurements with a max total error of approximately ±3% for <700 K environmental temperatures. The Δv1 emission is not ideal for standalone temperature measurements, having max total error of approximately 27%. The high measurement error of the Δv1 emission primarily stems from low temperatures and weak signal, suggesting that the band may be more suitable for higher temperature measurements.
One-dimensional capabilities are realized only through the removal of the spectrometer. The emission signal was fully integrated across the spectrum from approximately 375 to 435 nm to simulate direct imaging of the emissions with a camera. The non-discrete emission analysis yielded temperature measurements with accuracies similar to the discrete Δv0 band, having max total error of approximately 5%. Sets of resonant wavelengths ideal for various temperature ranges are given in Table 4. The ability to accurately measure gas-temperature via direct imaging of the $N_2^ + ({{B^2}\Sigma _u^ +{-} {X^2}\Sigma _g^ + } )$ transition allows not only 1D line capability, but reduces experimental setup time, optical complexity, associated costs, and space helping realize the techniques full potential. Furthermore, the non-discrete signal is sum of the discrete emissions increasing the overall signal intensity and SNR.
The 3-photon ${N_2}({{X^1}\mathrm{\Sigma }_g^ + ,v = 0 \to {b^1}{\mathrm{\Pi }_u},v = 6} )$ absorption band and REMPI mechanism that is used by N2 RIPT is collisional influenced, with a (3 + 1) scheme occurring at low pressure and a (3 + 2) scheme occurring near standard pressure conditions (approximately 14.7 psi [pounds per square inch]). The calibration study maintained standard pressure conditions across all measurement temperatures. However, the signal dependence on pressure maintains a linear relationship. Physically, as pressure increases so does the number density and availability of nitrogen molecules, thus signal generation is strengthened. However, as pressure further increases the collisional induced REMPI scheme results in a decrease in signal generation, but this is balanced by the increases in number density, thus maintaining a linear relationship. The drawback to N2 RIPT is four wavelengths are currently needed to probe the rotational state distribution and acquire enough information to fit signals to a Boltzmann distribution for accurate and repeatable temperature measurements.
Funding
U.S. Department of Energy; National Science Foundation.
Acknowledgment
This work is supported by University of Tennessee, NSF-2026242 and DOE DE-SC0021382. Data availability. Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Disclosures
The authors declare that there are no conflicts of interest related to this article.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
References
1. R. Miles, A. Dogariu, and L. Dogariu, “Localized time accurate sampling of nonequilibrium and unsteady hypersonic flows: methods and horizons,” Exp. Fluids 62(12), 248 (2021). [CrossRef]
2. W. McCord, A. Clark, and Z. Zhang, “One-dimensional air temperature measurements by air resonance enhanced multiphoton Ionization thermometry (ART),” Opt. Express 30(11), 18539–18551 (2022). [CrossRef]
3. P. M. Danehy, R. A. Burns, D. T. Reese, et al., “FLEET Velocimetry for Aerodynamics,” Annu. Rev. Fluid Mech. 54(1), 525–553 (2022). [CrossRef]
4. F. K. Lu, Advanced hypersonic test facilities (AIAA, 2002), Vol. 198.
5. A. W. Cary, J. Chawner, E. P. Duque, et al., “Cfd vision 2030 road map: Progress and perspectives,” in AIAA AVIATION 2021 FORUM, (2021), 2726.
6. I. A. Leyva, “The relentless pursuit of hypersonic flight,” Phys. Today 70(11), 30–36 (2017). [CrossRef]
7. C. Arisman, C. Johansen, B. Bathel, et al., “Investigation of gas seeding for planar laser-induced fluorescence in hypersonic boundary layers,” AIAA J. 53(12), 3637–3651 (2015). [CrossRef]
8. B. Balakumar, G. Orlicz, C. Tomkins, et al., “Simultaneous particle-image velocimetry–planar laser-induced fluorescence measurements of Richtmyer–Meshkov instability growth in a gas curtain with and without reshock,” Phys. Fluids 20(12), 124103 (2008). [CrossRef]
9. J. Li, B. Yu, W. Zhao, et al., “A review of signal enhancement and noise reduction techniques for tunable diode laser absorption spectroscopy,” Appl. Spectrosc. Rev. 49(8), 666–691 (2014). [CrossRef]
10. P. Werle, R. Mücke, and F. Slemr, “The limits of signal averaging in atmospheric trace-gas monitoring by tunable diode-laser absorption spectroscopy (TDLAS),” Appl. Phys. B 57(2), 131–139 (1993). [CrossRef]
11. R. B. Miles, W. R. Lempert, and J. N. Forkey, “Laser rayleigh scattering,” Meas. Sci. Technol. 12(5), R33–R51 (2001). [CrossRef]
12. A. Cutler, P. Danehy, R. Springer, et al., “Coherent anti-Stokes Raman spectroscopic thermometry in a supersonic combustor,” AIAA J. 41(12), 2451–2459 (2003). [CrossRef]
13. A. Clark, W. McCord, and Z. Zhang, “Air resonance enhanced multiphoton ionization tagging velocimetry,” Appl. Opt. 61(13), 3748 (2022). [CrossRef]
14. Y. Wu, M. Gragston, and Z. Zhang, “Acoustic detection of resonance-enhanced multiphoton ionization for spatially resolved temperature measurement,” Opt. Lett. 42(17), 3415–3418 (2017). [CrossRef]
15. J. Sawyer, Y. Wu, Z. Zhang, et al., “O2 rotational temperature measurements in an atmospheric air microdischarge by radar resonance-enhanced multiphoton ionization,” J. Appl. Phys. 113(23), 233304 (2013). [CrossRef]
16. Y. Wu, J. Sawyer, Z. Zhang, et al., “Flame Temperature Measurements by Radar REMPI of Molecular Oxygen,” Appl. Opt. 51(28), 6864 (2012). [CrossRef]
17. Y. Wu, M. Gragston, Z. Zhang, et al., “Spatially localized, see-through-wall temperature measurements in a flow reactor using radar REMPI,” Opt. Lett. 42(1), 53–56 (2017). [CrossRef]
18. Y. Wu, Z. Zhang, and S. F. Adams, “O2 rotational temperature measurements by coherent microwave scattering from REMPI,” Chem. Phys. Lett. 513(4-6), 191–194 (2011). [CrossRef]
19. H. K. Cheng, J. G. Hall, T. Golian, et al., “Boundary-layer displacement and leading-edge bluntness effects in high-temperature hypersonic flow,” Journal of the Aerospace Sciences 28(5), 353–381 (1961). [CrossRef]
20. J. C. Sivells, “Aerodynamic design of axisymmetric hypersonic wind-tunnel nozzles,” J. Spacecr. Rockets 7(11), 1292–1299 (1970). [CrossRef]
21. L. Trimmer, J. Cary, Aubrey, et al., “The optimum hypersonic wind tunnel,” in 14th Aerodynamic Testing Conference, (1968), 739.
22. D. Marren and J. Lafferty, “The AEDC hypervelocity wind tunnel 9,” Progress in Astronautics and Aeronautics 198, 467–478 (2002). [CrossRef]
23. S. Adams and J. Williamson, “Spectroscopic Study of N2(b(1)Πu, v=8) by atmospheric pressure resonant-enhanced multiphoton ionization and fluorescence detection,” J. Phys. Chem. A 117(50), 13535–13542 (2013). [CrossRef]
24. Z. Zhang, M. N. Shneider, and R. B. Miles, “Coherent microwave scattering from resonance enhanced multi-photon ionization (radar REMPI): a review,” Plasma Sources Sci. Technol. 30(10), 103001 (2021). [CrossRef]
25. Z. Zhang, M. N. Shneider, and R. B. Miles, “Coherent microwave rayleigh scattering from resonance-enhanced multiphoton ionization in argon,” Phys. Rev. Lett. 98(26), 265005 (2007). [CrossRef]
26. R. Bray and R.-M. Hochstrasser, “Two-photon absorption by rotating diatomic molecules,” Mol. Phys. 31(4), 1199–1211 (1976). [CrossRef]
27. P. M. Johnson and C. E. Otis, “Molecular multiphoton spectroscopy with ionization detection,” Annu. Rev. Phys. Chem. 32(1), 139–157 (1981). [CrossRef]
28. S. T. Pratt, P. M. Dehmer, and J. L. Dehmer, “Photoelectron studies of resonant multiphoton ionization of molecular nitrogen,” J. Chem. Phys. 81(8), 3444–3451 (1984). [CrossRef]
29. S. F. Adams, J. M. Williamson, and D. M. Fisher, “Rotational temperature analysis of N2 by resonant enhanced multi-photon ionization with fluorescence detection,” J. Appl. Phys. 110(8), 083309 (2011). [CrossRef]
30. A. Lofthus and P. H. Krupenie, “The spectrum of molecular nitrogen,” J. Phys. Chem. Ref. Data 6(1), 113–307 (1977). [CrossRef]
31. N. Van Veen, P. Brewer, P. Das, et al., “Detection of the a 1Π g (v′= 0, 1)← X 1Σ+ g (v ″= 0) transition in N2 by laser-induced fluorescence,” J. Chem. Phys. 77(9), 4326–4329 (1982). [CrossRef]
32. M. Aldén and W. Wendt, “Detection of nitrogen molecules through multi-photon laser excitation and N+ 2 fluorescence,” Opt. Commun. 69(1), 31–36 (1988). [CrossRef]
33. S. Adams, C. DeJoseph Jr, and J. Williamson, “Formation and electron-ion recombination of N 4 + following photoionization in near-atmospheric pressure N 2,” J. Chem. Phys. 130(14), 144316 (2009). [CrossRef]
34. A. Kvaran, B. G. Waage, and H. Wang, “What to see and what not to see in three-photon absorption:(3 + 1) REMPI of HBr,” J. Chem. Phys. 113(5), 1755–1761 (2000). [CrossRef]
35. S. McGuire and R. Miles, “Collision induced ultraviolet structure in nitrogen radar REMPI spectra,” J. Chem. Phys. 141(24), 244301 (2014). [CrossRef]
36. C. Kaminski, B. Löfstedt, R. Fritzon, et al., “Two-photon polarization spectroscopy and (2 + 3)-photon laser induced fluorescence of N2,” Opt. Commun. 129(1-2), 38–43 (1996). [CrossRef]
37. J. Halpern, H. Zacharias, and R. Wallenstein, “Rotational line strengths in two-and three-photon transitions in diatomic molecules,” J. Mol. Spectrosc. 79(1), 1–30 (1980). [CrossRef]
38. G. Herzberg, Molecular Spectra and Molecular Structure (Read Books, 2008).
